In [6]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import warnings
warnings.filterwarnings("ignore")
In [7]:
data = pd.read_csv("student-mat.csv", sep = ';') # student math score file
In [8]:
data.head()
Out[8]:
school sex age address famsize Pstatus Medu Fedu Mjob Fjob ... famrel freetime goout Dalc Walc health absences G1 G2 G3
0 GP F 18 U GT3 A 4 4 at_home teacher ... 4 3 4 1 1 3 6 5 6 6
1 GP F 17 U GT3 T 1 1 at_home other ... 5 3 3 1 1 3 4 5 5 6
2 GP F 15 U LE3 T 1 1 at_home other ... 4 3 2 2 3 3 10 7 8 10
3 GP F 15 U GT3 T 4 2 health services ... 3 2 2 1 1 5 2 15 14 15
4 GP F 16 U GT3 T 3 3 other other ... 4 3 2 1 2 5 4 6 10 10

5 rows × 33 columns

In [9]:
data.shape
Out[9]:
(395, 33)
In [10]:
data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 395 entries, 0 to 394
Data columns (total 33 columns):
 #   Column      Non-Null Count  Dtype 
---  ------      --------------  ----- 
 0   school      395 non-null    object
 1   sex         395 non-null    object
 2   age         395 non-null    int64 
 3   address     395 non-null    object
 4   famsize     395 non-null    object
 5   Pstatus     395 non-null    object
 6   Medu        395 non-null    int64 
 7   Fedu        395 non-null    int64 
 8   Mjob        395 non-null    object
 9   Fjob        395 non-null    object
 10  reason      395 non-null    object
 11  guardian    395 non-null    object
 12  traveltime  395 non-null    int64 
 13  studytime   395 non-null    int64 
 14  failures    395 non-null    int64 
 15  schoolsup   395 non-null    object
 16  famsup      395 non-null    object
 17  paid        395 non-null    object
 18  activities  395 non-null    object
 19  nursery     395 non-null    object
 20  higher      395 non-null    object
 21  internet    395 non-null    object
 22  romantic    395 non-null    object
 23  famrel      395 non-null    int64 
 24  freetime    395 non-null    int64 
 25  goout       395 non-null    int64 
 26  Dalc        395 non-null    int64 
 27  Walc        395 non-null    int64 
 28  health      395 non-null    int64 
 29  absences    395 non-null    int64 
 30  G1          395 non-null    int64 
 31  G2          395 non-null    int64 
 32  G3          395 non-null    int64 
dtypes: int64(16), object(17)
memory usage: 102.0+ KB

Data set Explanation¶

The following are the explanations for the column names:

  1. Demographic Information:

    • school: School name. ('GP' - Gabriel Pereira or 'MS' - Mousinho da Silveira)
    • sex: Student's gender. ('F' - female or 'M' - male)
    • age: Student's age.
    • address: Type of address ('U' - urban or 'R' - rural).
    • famsize: Family size. ('LE3' - less or equal to 3 or 'GT3' - greater than 3)
    • Pstatus: Parent's cohabitation status. ('T' - living together or 'A' - apart)

  2. Educational Background:

    • Medu: Mother's education level.
    • Fedu: Father's education level.
    • Mjob: Mother's job.
    • Fjob: Father's job.

  3. Reasons for Choosing School:

    • reason: Reason for choosing the school.

  4. Guardian Information:

    • guardian: Student's guardian.

  5. Time Factors:

    • traveltime: Travel time to school from home.
    • studytime: Weekly study time.

  6. Academic Performance:

    • failures: Number of past class failures.
    • schoolsup: Extra educational support from the school.
    • famsup: Family educational support.
    • paid: Extra paid classes within the course subject (Math or Portuguese).
    • activities: Extra-curricular activities.
    • nursery: Attended at nursery school.
    • higher: Plans to pursue higher education.
    • internet: Internet access at home.
    • romantic: In a romantic relationship.

  7. Social and Personal Life:

    • famrel: Quality of family relationships.
    • freetime: Free time after school.
    • goout: Going out with friends.
    • Dalc: Workday alcohol consumption.
    • Walc: Weekend alcohol consumption.
    • health: Current health status.

  8. Attendance and Grades:

    • absences: Number of school absences.

    • G1, G2, G3: Grades in three different periods.

    • G1 - first period grade (numeric: from 0 to 20) - Maths

    • G2 - second period grade (numeric: from 0 to 20) - Portuguese
    • G3 - final grade (numeric: from 0 to 20, output target) - combination of first two subjects

Renaming the columns¶

In [11]:
column_names = {
    'school': 'School',
    'sex': 'Gender',
    'age': 'Age',
    'address': 'Address',
    'famsize': 'Family_Size',
    'Pstatus': 'Parent_Cohabitation_Status',
    'Medu': 'Mother_Education',
    'Fedu': 'Father_Education',
    'Mjob': 'Mother_Job',
    'Fjob': 'Father_Job',
    'reason': 'Reason_for_Choosing_School',
    'guardian': 'Guardian',
    'traveltime': 'Travel_Time',
    'studytime': 'Study_Time',
    'failures': 'Past_Failures',
    'schoolsup': 'School_Support',
    'famsup': 'Family_Support',
    'paid': 'Paid_Classes',
    'activities': 'Extra_Curricular_Activities',
    'nursery': 'Nursery_Attendance',
    'higher': 'Plans_for_Higher_Education',
    'internet': 'Internet_Access',
    'romantic': 'In_Relationship',
    'famrel': 'Family_Relationship_Quality',
    'freetime': 'Free_Time',
    'goout': 'Go_Out_with_Friends',
    'Dalc': 'Workday_Alcohol_Consumption',
    'Walc': 'Weekend_Alcohol_Consumption',
    'health': 'Health_Status',
    'absences': 'Absences',
    'G1': 'Grade_Period_1',
    'G2': 'Grade_Period_2',
    'G3': 'Grade_Period_3'
}

data.rename(columns=column_names, inplace=True)

data.columns = data.columns.str.lower()
In [12]:
data.columns
Out[12]:
Index(['school', 'gender', 'age', 'address', 'family_size',
       'parent_cohabitation_status', 'mother_education', 'father_education',
       'mother_job', 'father_job', 'reason_for_choosing_school', 'guardian',
       'travel_time', 'study_time', 'past_failures', 'school_support',
       'family_support', 'paid_classes', 'extra_curricular_activities',
       'nursery_attendance', 'plans_for_higher_education', 'internet_access',
       'in_relationship', 'family_relationship_quality', 'free_time',
       'go_out_with_friends', 'workday_alcohol_consumption',
       'weekend_alcohol_consumption', 'health_status', 'absences',
       'grade_period_1', 'grade_period_2', 'grade_period_3'],
      dtype='object')
In [13]:
data.isnull().sum()
Out[13]:
school                         0
gender                         0
age                            0
address                        0
family_size                    0
parent_cohabitation_status     0
mother_education               0
father_education               0
mother_job                     0
father_job                     0
reason_for_choosing_school     0
guardian                       0
travel_time                    0
study_time                     0
past_failures                  0
school_support                 0
family_support                 0
paid_classes                   0
extra_curricular_activities    0
nursery_attendance             0
plans_for_higher_education     0
internet_access                0
in_relationship                0
family_relationship_quality    0
free_time                      0
go_out_with_friends            0
workday_alcohol_consumption    0
weekend_alcohol_consumption    0
health_status                  0
absences                       0
grade_period_1                 0
grade_period_2                 0
grade_period_3                 0
dtype: int64
In [14]:
# checking for duplicates

duplicate_rows = data.duplicated()
total_duplicates = data.duplicated().sum()
total_duplicates
Out[14]:
0
In [15]:
data[duplicate_rows]
Out[15]:
school gender age address family_size parent_cohabitation_status mother_education father_education mother_job father_job ... family_relationship_quality free_time go_out_with_friends workday_alcohol_consumption weekend_alcohol_consumption health_status absences grade_period_1 grade_period_2 grade_period_3

0 rows × 33 columns

Checking for Correlation¶

In [16]:
# looking for correlations

numeric_columns = data.select_dtypes(include=['int64', 'float64']).columns

corr_matrix = data[numeric_columns].corr()
plt.figure(figsize=(10,10))
sns.heatmap(corr_matrix, annot = True, cmap = 'coolwarm', fmt = ".2f")
plt.show()
  1. There are no strong correlations (either positive or negative) between the numeric columns in the data set.
  2. There are very few strong correlations which are completely meaningless for certain analysis.

Summary of the dataset¶

In [17]:
summary = data.describe()
In [18]:
summary
Out[18]:
age mother_education father_education travel_time study_time past_failures family_relationship_quality free_time go_out_with_friends workday_alcohol_consumption weekend_alcohol_consumption health_status absences grade_period_1 grade_period_2 grade_period_3
count 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000 395.000000
mean 16.696203 2.749367 2.521519 1.448101 2.035443 0.334177 3.944304 3.235443 3.108861 1.481013 2.291139 3.554430 5.708861 10.908861 10.713924 10.415190
std 1.276043 1.094735 1.088201 0.697505 0.839240 0.743651 0.896659 0.998862 1.113278 0.890741 1.287897 1.390303 8.003096 3.319195 3.761505 4.581443
min 15.000000 0.000000 0.000000 1.000000 1.000000 0.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 0.000000 3.000000 0.000000 0.000000
25% 16.000000 2.000000 2.000000 1.000000 1.000000 0.000000 4.000000 3.000000 2.000000 1.000000 1.000000 3.000000 0.000000 8.000000 9.000000 8.000000
50% 17.000000 3.000000 2.000000 1.000000 2.000000 0.000000 4.000000 3.000000 3.000000 1.000000 2.000000 4.000000 4.000000 11.000000 11.000000 11.000000
75% 18.000000 4.000000 3.000000 2.000000 2.000000 0.000000 5.000000 4.000000 4.000000 2.000000 3.000000 5.000000 8.000000 13.000000 13.000000 14.000000
max 22.000000 4.000000 4.000000 4.000000 4.000000 3.000000 5.000000 5.000000 5.000000 5.000000 5.000000 5.000000 75.000000 19.000000 19.000000 20.000000

Proportion of students with two parents who work, one parent who works, no parents who work¶

In [19]:
data.shape
Out[19]:
(395, 33)
In [21]:
import matplotlib.pyplot as plt
import numpy as np

work_columns = ['mother_job', 'father_job']
working_parents = data[work_columns]

counts = working_parents.apply(lambda x: '_'.join(x), axis=1).value_counts()
In [22]:
counts
Out[22]:
other_other          104
services_services     43
services_other        42
at_home_other         33
other_services        24
teacher_other         21
teacher_services      19
health_other          17
at_home_services      15
teacher_teacher       12
health_services       10
services_teacher       8
at_home_at_home        7
health_health          6
other_teacher          6
services_at_home       6
other_at_home          5
services_health        4
teacher_health         4
at_home_teacher        2
other_health           2
teacher_at_home        2
at_home_health         2
health_teacher         1
dtype: int64
In [23]:
working_parents
Out[23]:
mother_job father_job
0 at_home teacher
1 at_home other
2 at_home other
3 health services
4 other other
... ... ...
390 services services
391 services services
392 other other
393 services other
394 other at_home

395 rows × 2 columns

In [24]:
counts.sum()
Out[24]:
395
In [25]:
no_parents_work = counts.get('at_home_at_home', 0)

one_parent_works = (
    counts.get('at_home_other', 0) +
    counts.get('at_home_services', 0) +
    counts.get('at_home_teacher', 0) +
    counts.get('at_home_health', 0) +
    counts.get('other_at_home', 0) +
    counts.get('services_at_home', 0) +
    counts.get('teacher_at_home', 0) +
    counts.get('health_at_home', 0)
)

total_entries = sum(counts.values)
two_parents_work = total_entries - (no_parents_work + one_parent_works)
In [26]:
print('no_parents_work:' ,no_parents_work)
print('one_parent_works:' ,one_parent_works)
print('two_parents_work:' ,two_parents_work)

no_parents_work: 7
one_parent_works: 65
two_parents_work: 323
In [27]:
import plotly.graph_objects as go

categories = ['Two Parents Work', 'One Parent Works', 'No Parents Work']
values = [two_parents_work, one_parent_works, no_parents_work, two_parents_work]  # Repeat the first value

total_students = len(data)
proportions = [100 * value / total_students for value in values] 

fig = go.Figure()

fig.add_trace(go.Scatterpolar(
    r=proportions + proportions[:1] + ['%'],
    theta=categories + [categories[0]],
    fill='toself',
    name='Proportion of Students',
    
))

fig.update_layout(
    polar=dict(
        radialaxis=dict(visible=False),
    ),
    showlegend=False,
    title=dict(text="Proportion of Students with Working Parents", x=0.5, y=0.9, xanchor='center', yanchor='top')
)

fig.show()

We can interpret from the triangle that

  1. The proportion of children with their both parents work is very high (81.77%) in the given data set since the point is the farthest or the length of the line is the lengthiest among all the three.
  2. The proportion of children with their both parents not working is very low which is (1.77%)
  3. The proportion of children wither either one of the parents working is average which is around (16.5%)

We can conclude that most of the children parents are employed and only very few children have their parents who are un-employed which might or might not affect their grades. There are many factors at this point of time that have to be analyzed about the children whose parents aren't working

In [28]:
import seaborn as sns
import matplotlib.pyplot as plt

# Create a new column in the DataFrame to represent the parental work situation
data['parental_work_situation'] = working_parents.apply(
    lambda x: 
        'Two Parents Work' if x['mother_job'] != 'at_home' and x['father_job'] != 'at_home' 
        else 'One Parent Works' if (x['mother_job'] != 'at_home' and x['father_job'] == 'at_home') or (x['mother_job'] == 'at_home' and x['father_job'] != 'at_home') 
        else 'No Parents Work' if x['mother_job'] == 'at_home' and x['father_job'] == 'at_home'
        else 'Other',  # Add an 'Other' category for unexpected cases
    axis=1
)


# Define the order of categories
category_order = ['Two Parents Work', 'One Parent Works', 'No Parents Work']

# Plotting box plots
plt.figure(figsize=(12, 8))
sns.boxplot(x='parental_work_situation', y='grade_period_3', data=data, order=category_order)
plt.title('Relationship between Parental Work Situation and G3')
plt.show()

We can see that the median of the children with both the parents work is obviously higher that children with only single parent works.

But surprisingly the median of the children with both the parents donot work is very high compared to the other two. This might indicate the children are working hard whose parents don't have any employement and are achieving highest grades.

All three categories have the lowest possible outlier 0

Pie charts of Family support and parents cohabitation status¶

In [29]:
import matplotlib.pyplot as plt

Family_support = data['family_support'].value_counts()
cohabitation_counts = data['parent_cohabitation_status'].value_counts()

# Giving custom labels for each category
cohabitation_labels = ['Living Together', 'Living Apart']
family_support_labels = [ 'Family Support', 'No Support',]

plt.figure(figsize=(10, 5))

plt.subplot(1, 2, 1)
plt.pie(cohabitation_counts, labels=cohabitation_labels, autopct='%1.1f%%', colors=['lightskyblue', 'Purple'])
plt.title('Parental Cohabitation Status')

plt.subplot(1, 2, 2)
plt.pie(Family_support, labels=family_support_labels, autopct='%1.1f%%', colors=['lightskyblue', 'Purple'])
plt.title('Family Support')

plt.tight_layout()

plt.show()

Figure depicts the distribution of students according to the “Parental Cohabitation Status” and “Family Support”. The first pie chart illustrates that the majority of the students have their parents living together which contributes to nearly 90% of the students, whereas only 10% of the students' parents are living apart. The second pie chart illustrates that 61% of the students are supported by their parents for their education and the rest of them are not supported.

Layered Histogram - Distribution of overall math scores by parent work status.¶

In [30]:
import matplotlib.pyplot as plt

custom_palette = ['skyblue', 'salmon'] 

plt.figure(figsize=(12, 6))

for i, status in enumerate(data['parent_cohabitation_status'].unique()):
    data_subset = data[data['parent_cohabitation_status'] == status]['grade_period_3']
    plt.hist(data_subset, bins=20, alpha=0.5, label=f'Parent Cohabitation: {status}', color=custom_palette[i])

plt.title('Histogram of Math Scores by Parent Cohabitation Status')
plt.xlabel('Math Score (G3)')
plt.ylabel('Frequency')
plt.legend()
plt.show()

We can see from Figure that most of the parents are living together and hence the pink part of the visualization is huge compared to the blue part which is behind the pink ones. It can be seen that most of the students have scored the median mark which is 10 - 11. There are some students who got 0 in the final grade which is a limitation and has to be further analyzed.

Distribution of Math scores according to Parental Cohabitation Status (Density plot)¶

In [31]:
import seaborn as sns
import matplotlib.pyplot as plt

custom_palette = ['skyblue', 'salmon'] 

plt.figure(figsize=(12, 6))

if (data['grade_period_3'] < 0).any():
    raise ValueError("Negative values found in 'G3' column.")

for i, status in enumerate(data['parent_cohabitation_status'].unique()):
    sns.kdeplot(data[data['parent_cohabitation_status'] == status]['grade_period_3'], label=f'Parent Cohabitation: {status}', shade=True, color=custom_palette[i], bw_adjust=1.0)

plt.title('Distribution of Math Scores by Parent Cohabitation Status')
plt.xlabel('Math Score (G3)')
plt.ylabel('Density')
plt.legend()
plt.show()

The main aim of the density plot is to visualize the mean and median of the particular column and also decide whether the values in that particular column are normally distributed or not. Looking into the graph, we can see that both of the categories have the mean almost equal and same. The shapes of the graphs are almost similar. The range of math scores is from 0 to 20 according to the data set. But due to flattening and smoothing of data it appears that the scores start from -5 and end at 25 which is only for the purpose of plotting the graph.

In [26]:
data['parent_cohabitation_status'].value_counts()
Out[26]:
parent_cohabitation_status
T    354
A     41
Name: count, dtype: int64

Box and Whisker Plot - Relationship with family and math score.¶

In [32]:
plt.figure(figsize=(10, 6))
sns.boxplot(x='family_relationship_quality', y='grade_period_3', data=data, palette='Blues')
plt.title('Relationship with Family and Math Score')
plt.xlabel('Family Relationship Quality')
plt.ylabel('Math Score (G3)')
plt.show()

Figure illustrates the distribution of math scores for each possible scale of Family Relationship Quality. The Family Relationship is measured on a scale of 1 to 5 where 1 being the lowest and 5 being the highest. We can observe that there is no specific relationship or trend that is being followed in the graph. At this point of time we can’t conclude anything without solid statistical evidence. The median of scores is decreasing from 1 to 3 whereas it started increasing from 3 to 5.

An independent two-sample z-test to examine if there is a significant difference in the mean of student grades between two groups ("Parents living together" and "Parents living apart")¶

In [33]:
from scipy.stats import norm

def z_test(series1, series2):
    # Calculate the mean and standard deviation of the two series
    mean1 = series1.mean()
    mean2 = series2.mean()
    std1 = series1.std()
    std2 = series2.std()
    
    # Calculate the standard error of the difference in means
    se = ((std1**2) / len(series1) + (std2**2) / len(series2))**0.5
    
    # Calculate the z-statistic
    z = (mean1 - mean2) / se
    
    # Calculate the p-value
    p_value = 2 * (1 - norm.cdf(abs(z)))
    
    return z, p_value
In [43]:
from statsmodels.stats.weightstats import ztest

group1 = data[data['parent_cohabitation_status'] == 'T']['grade_period_3']  # Parents living together
group2 = data[data['parent_cohabitation_status'] == 'A']['grade_period_3']  # Parents living apart

statistic, p_value = ztest(group1, x2=group2, alternative='two-sided', usevar='pooled', value=abs(np.mean(group1) - np.mean(group2)))

mean_group1 = np.mean(group1)
mean_group2 = np.mean(group2)
std_dev_group1 = np.std(group1)
std_dev_group2 = np.std(group2)

# Calculating the confidence interval
ci_low, ci_high = (mean_group1 - mean_group2) - 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2)), \
                  (mean_group1 - mean_group2) + 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2))

# Printing results
print(f"P-value for Parent Cohabitation Status: {p_value}")
print(f"Confidence Interval: ({ci_low:.2f}, {ci_high:.2f})")
print(f"Mean (Parents living together: yes): {mean_group1:.2f}")
print(f"Mean (Parents living together: no): {mean_group2:.2f}")
print(f"Standard Deviation (Parents living together: yes): {std_dev_group1:.2f}")
print(f"Standard Deviation (Parents living together: no): {std_dev_group2:.2f}")

P-value for Parent Cohabitation Status: 0.021231279886913746
Confidence Interval: (-2.25, 0.51)
Mean (Parents living together: yes): 10.32
Mean (Parents living together: no): 11.20
Standard Deviation (Parents living together: yes): 4.60
Standard Deviation (Parents living together: no): 4.24

Same test for Non-Adults (Parents living together vs. Parents living apart)¶

In [34]:
from statsmodels.stats.weightstats import ztest

df_copy = data[data['age'] < 18]

group1 = df_copy[df_copy['parent_cohabitation_status'] == 'T']['grade_period_3']  # Parents living together
group2 = df_copy[df_copy['parent_cohabitation_status'] == 'A']['grade_period_3']  # Parents living apart

statistic, p_value = ztest(group1, x2=group2, alternative='two-sided', usevar='pooled', value=abs(np.mean(group1) - np.mean(group2)))

mean_group1 = np.mean(group1)
mean_group2 = np.mean(group2)
std_dev_group1 = np.std(group1)
std_dev_group2 = np.std(group2)
# Calculate the confidence interval
ci_low, ci_high = (mean_group1 - mean_group2) - 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2)), \
                  (mean_group1 - mean_group2) + 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2))

# Print results
print(f"P-value for Parent Cohabitation Status: {p_value}")
print(f"Confidence Interval: ({ci_low:.2f}, {ci_high:.2f})")
print(f"Mean (Parents living together: yes): {mean_group1:.2f}")
print(f"Mean (Parents living together: no): {mean_group2:.2f}")
print(f"Standard Deviation (Parents living together: yes): {std_dev_group1:.2f}")
print(f"Standard Deviation (Parents living together: no): {std_dev_group2:.2f}")

P-value for Parent Cohabitation Status: 0.9219454729056976
Confidence Interval: (-1.68, 1.59)
Mean (Parents living together: yes): 10.83
Mean (Parents living together: no): 10.87
Standard Deviation (Parents living together: yes): 4.37
Standard Deviation (Parents living together: no): 4.38
In [33]:
## Same test for Adults (Parents living together vs. Parents living apart)
In [35]:
from statsmodels.stats.weightstats import ztest

df_copy = data[data['age'] > 18]

group1 = df_copy[df_copy['parent_cohabitation_status'] == 'T']['grade_period_3']  # Parents living together
group2 = df_copy[df_copy['parent_cohabitation_status'] == 'A']['grade_period_3']  # Parents living apart

statistic, p_value = ztest(group1, x2=group2, alternative='two-sided', usevar='pooled', value=abs(np.mean(group1) - np.mean(group2)))

mean_group1 = np.mean(group1)
mean_group2 = np.mean(group2)
std_dev_group1 = np.std(group1)
std_dev_group2 = np.std(group2)
# Calculate the confidence interval
ci_low, ci_high = (mean_group1 - mean_group2) - 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2)), \
                  (mean_group1 - mean_group2) + 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2))

# Print results
print(f"P-value for Parent Cohabitation Status: {p_value}")
print(f"Confidence Interval: ({ci_low:.2f}, {ci_high:.2f})")
print(f"Mean (Parents living together: yes): {mean_group1:.2f}")
print(f"Mean (Parents living together: no): {mean_group2:.2f}")
print(f"Standard Deviation (Parents living together: yes): {std_dev_group1:.2f}")
print(f"Standard Deviation (Parents living together: no): {std_dev_group2:.2f}")

P-value for Parent Cohabitation Status: 0.00013784392530664805
Confidence Interval: (-8.35, -0.91)
Mean (Parents living together: yes): 8.12
Mean (Parents living together: no): 12.75
Standard Deviation (Parents living together: yes): 4.49
Standard Deviation (Parents living together: no): 3.34

An independent two-sample z-test to examine if there is a significant difference in the mean of student grades between two groups ("With family support" and "Without family support")¶

In [36]:
from statsmodels.stats.weightstats import ztest

group1 = data[data['family_support'] == 'yes']['grade_period_3']  # Family support: yes
group2 = data[data['family_support'] == 'no']['grade_period_3']   # Family support: no

statistic, p_value = ztest(group1, x2=group2, alternative='two-sided', usevar='pooled', value=abs(np.mean(group1) - np.mean(group2)))

mean_group1 = np.mean(group1)
mean_group2 = np.mean(group2)
std_dev_group1 = np.std(group1)
std_dev_group2 = np.std(group2)

# Calculating the confidence interval
ci_low, ci_high = (mean_group1 - mean_group2) - 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2)), \
                  (mean_group1 - mean_group2) + 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2))

# Printing results
print(f"P-value for Family Support: {p_value}")
print(f"Confidence Interval: ({ci_low:.2f}, {ci_high:.2f})")
print(f"Mean (Family Support: yes): {mean_group1:.2f}")
print(f"Mean (Family Support: no): {mean_group2:.2f}")
print(f"Standard Deviation (Family Support: yes): {std_dev_group1:.2f}")
print(f"Standard Deviation (Family Support: no): {std_dev_group2:.2f}")

P-value for Family Support: 0.12025314965674688
Confidence Interval: (-1.30, 0.56)
Mean (Family Support: yes): 10.27
Mean (Family Support: no): 10.64
Standard Deviation (Family Support: yes): 4.54
Standard Deviation (Family Support: no): 4.62

An independent two-sample z-test to examine if there is a significant difference in the mean of student grades between two groups (Good Family relationship vs Not Good Family relationship)¶

In [37]:
from statsmodels.stats.weightstats import ztest

group1 = data[data['family_relationship_quality']<4]['grade_period_3']  # Not good Family relationship
group2 = data[data['family_relationship_quality']>=4]['grade_period_3']   # Good Family relationship

# Perform the two-tailed z-test
statistic, p_value = ztest(group1, x2=group2, alternative='two-sided', usevar='pooled', value=abs(np.mean(group1) - np.mean(group2)))

mean_group1 = np.mean(group1)
mean_group2 = np.mean(group2)
std_dev_group1 = np.std(group1)
std_dev_group2 = np.std(group2)
# Calculate the confidence interval
ci_low, ci_high = (mean_group1 - mean_group2) - 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2)), \
                  (mean_group1 - mean_group2) + 1.96 * np.sqrt(std_dev_group1**2/len(group1) + std_dev_group2**2/len(group2))

# Print results
print(f"P-value for Family Relationship status: {p_value}")
print(f"Confidence Interval: ({ci_low:.2f}, {ci_high:.2f})")
print(f"Mean (Bad Family Relationship): {mean_group1:.2f}")
print(f"Mean (Good Family Relationship): {mean_group2:.2f}")
print(f"Standard Deviation (Bad Family Relationship): {std_dev_group1:.2f}")
print(f"Standard Deviation (Good Family Relationship): {std_dev_group2:.2f}")

P-value for Family Relationship status: 0.08857309537975457
Confidence Interval: (-1.55, 0.63)
Mean (Bad Family Relationship): 10.06
Mean (Good Family Relationship): 10.52
Standard Deviation (Bad Family Relationship): 4.77
Standard Deviation (Good Family Relationship): 4.51

THANK YOU...¶

In [ ]: